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Unformatted text preview: Chem 3890 Physical Chemistry I Fall 2010 Chemistry 3890 Problem Set 3 Fall 2010 Due: in class, Friday, September 24 Last revised: September 17, 2010 Useful tip : To clear global variables, use Remove["Global ` * "] Problem 1 In this problem we determine the properties of general Gaussian wavepackets. Define a wave- function ( x ) = A e ikx e- ( x- x ) 2 / 2 (1) depending on parameters k , and x , where k , and x are real, and A is a (real) normalization constant. 1. Calculate the normalization constant A for general ( k, , x ). Use the normalized for the rest of the problem. 2. Calculate ( x ) , ( x 2 ) and x for general ( k, , x ). Do your answers depend on k ? On ? 3. Calculate ( p ) , ( p 2 ) and p for general ( k, , x ). (Do not use the numerical value for planckover2pi1 ; keep your answer in symbolic form.) 4. Calculate the uncertainty product x p for general ( k, x ). Does your expression depend on the parameters k , or x ? As you can see, the wavefunctions ( x ) are very useful in that the mean (expectation) values of position and momentum can be dialled in through the choice of parameters x and k ....
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